Gravity and Topographic Data Processing

Summary

From the mid-1980s to 1990 the author worked on the gravity of Eastern Indonesia while studying for a Ph.D. at University College, London (UCL) supervised by Dr. John Milsom. Dr. Milsom had already collected much of the data for Timor, listed on the Data Sources page, but the author and co-workers surveyed the island groups of Tanimbar and Kai. A description of this earlier work can be found in the author's thesis (16.5meg PDF).

The gravity images and maps shown on this web site result from work to further correct, re-level and re-compute the original UCL data and merge these with the latest gravity and topographic data derived from satellite studies. All topography and gravity data, both on and off-shore, have been reduced to the latest ellipsoidal standard, meaning that the anomaly values are for gravity stations placed on the surface (on a hill, in a valley) relative to the International Terrestrial Reference Frame (ITRF(WGS84)) reference ellipsoid and not to the geoid.

The latest work results in gravity images and maps that are very much improved, compared to the original UCL work, especially for the land surveys of Timor, Tanimbar and Kai. However, the new UCL data should be characterised as regional in nature due to uncertainties and unknowns, i.e. errors, inherent in the retrieval of old, in some cases incomplete, data surveys in an age before GPS systems provided position and height fixes. It should not be assumed, because the data are now reduced to the latest geophysical and geodesic standards, that the original errors have been removed and that the data are now more precise and accurate.

Nevertheless, these data can be viewed as creating gravity surfaces that are, for the most part, coherent.

The new, ellipsoidal gravity data, referenced to ITRF(WGS84) and including the free-air and complete Bouguer anomalies (derived from a gridded surface), can be downloaded from the Data Sources page.

What now follows is a detailed description of the steps taken to produce the new, 2011, ellipsoidal dataset.

 

Topography

The topography dataset used is version 13.1 (date September 2010) of Sandwell and Smith's global predicted depth at 1 arc minute resolution combined with the high resolution (90metre) land elevations from the NASA Shuttle Radar Topography Mission (SRTM) processed by the International Centre for Tropical Agriculture (CIAT).

Sandwell and Smith: http://topex.ucsd.edu/WWW_html/mar_topo.html.

CIAT: http://srtm.csi.cgiar.org.

At 1 arc minute resolution the two datasets merge at the coastline with little mismatching - typically 3-5 metres except in areas with steep, or rapidly varying, gradients.

In the past the author has re-worked the Sandwell and Smith data to try and remove ship-tracks that criss-cross the area. This results in a lot of work which, although beneficial, is short-term as new iterations of the data are made available. Therefore the latest image and maps on this web site use the 'raw' Sandwell and Smith data which in places results in ship-tracks showing through on the gravity anomaly maps. Typically these ship-tracks have a topography range of 3-15 metres but some are much larger. Viewers interested in particular marine Bouguer anomalies are advised to cross-check the features with the topography and/or free-air maps.

For most of the study area the combined topography, at 1 minute resolution and referenced to the ITRF(WGS84) ellipsoid, was used to compute the complete Bouguer anomalies.However, on Timor, Tanimbar and Kai the high resolution SRTM (90metre) data were used.

Geoid undulation data (required to calculate the local ellipsoid) were calculated from the Earth Gravitational Model EGM2008 published by the National Geospacial-Intelligence Agency (NGA).

 

Eastern Timor preparation work

A description of the original UCL data sources and processing can be found on the Data Sources page. This map shows the station distribution for eastern and western Timor.

Some years ago the author noticed that the location of the island of Timor, according to earlier UCL work and most global coastline datasets, is different to that shown by the SRTM data. The SRTM data essentially form the best dataset for the location of land masses and is used by most modern mapping systems, e.g. Google Earth. The old location of Timor is probably based on the earlier 1970s topographic surveying by the then Portuguese administration (see Data Sources) and this work may have been passed through to the CIA World Map which has subsequently been used by many other mapping agencies.

The difference in location is approximately 1km, i.e. the 'old' Timor is 1km south of the SRTM Timor, a difference too great to be due to projection changes. The reason for this large disparity is not known to the author. Additionally, many of the islands in Eastern Indonesia, shown on old maps, were also not properly located by amounts that vary considerably. This is not surprising given the large, essentially marine area and the lack of systematic surveying of the island groups by a unitary surveying authority.

The 1km off-set of 'old' Timor also exists in the original UCL gravity datasets. As the latest, ellipsoidal gravity reduction work would place the gravity stations on the ITRF(WGS84) ellipsoid and the terrain corrections would use SRTM elevation data, it was necessary to relocate the UCL stations northwards by approximately 1km to match the SRTM data. The result is that coastal stations are now nearer the coast, mountain top stations are close to the highest points and other stations now more faithfully follow roads and old tracks visible on, for example, Google Earth.

No orthometric elevations or observed gravity values have been altered following this re-location.

 

Western Timor preparation work

The gravity data for western Timor were extracted by the author from the published Bouguer anomaly map while at UCL - see Data Sources. The contours were digitised, along with the station locations. The anomaly gradients between contours were then used to calculate the Bouguer anomalies at stations. Naturally, this process introduces unknown errors. However, errors are likely to be small and not significant for a regional survey. Further details are given in the author's thesis.

Western Timor is also incorrectly located on the old topographic maps, but not to the same extent as eastern Timor. After examining the western Timor gravity stations on Google Earth they were all moved 212 metres in a SE direction.

New heights were extracted from the STRM 90 metre dataset for the new positions.

 

Tanimbar and Kai Islands preparation work

The author, along with co-workers, gathered the gravity data for Tanimbar and Kai in 1987 and 1989 (see Data Sources). Tanimbar stations are shown on this map; Kai stations here.

At that time GPS was new, position gathering equipment was expensive, height estimates were either unavailable or very suspect and the GPS satellite coverage in Eastern Indonesia was very patchy, especially through the jungle canopy. Consequently positional information for gravity stations was either taken from old 1:250,000 scale topographic maps (the only available) when surveying the coast or estimated from pace and bearing information when traversing the islands. Heights were estimated from the topographic maps and barometric altimeters.

Errors in position and height for the gravity stations were estimated in the author's thesis. The maximum error of 3mGal on Tanimbar is due to height estimation at inland stations surveyed during the late afternoon. The Kai Islands, where most of the gravity stations were placed on the coast, will have a lower maximum anomaly error due to height estimation errors.

Like Timor, the islands of Tanimbar and Kai are misplaced relative to the modern SRTM dataset and Google Earth satellite images but this error is random, with differing displacements for individual islands and island groups. Consequently there is no 'global' movement of the old gravity stations that could place them all in a correct position with respect to the satellite/SRTM imagery. Also, the inland stations, those gathered when pacing and taking hand-held compass bearings, were often not located correctly with reference to the topography displayed on Google Earth images, e.g. stations that were established in river valleys might be shown on ridges in Google Earth.

For these reasons all the Tanimbar and Kai gravity stations have been individually relocated in Google Earth using the author's original survey notes and new heights taken from the STRM 90 metre data.

(Note: it might be thought that the station locations and heights are now more correct than they were in the late 1980's but this cannot be quantified or proven. Nevertheless, the author considers that the inland Tanimbar gravity stations are now placed more correctly.)

 

New gravity reduction to modern ellipsoidal standard

After the preparatory steps described above the historical, UCL, gravity stations for Timor, Tanimbar and Kai have new positions and heights (except for Eastern Timor) related to the latest satellite imagery and SRTM data. This places the stations in new positions related to the geoid.

All stations have original observed gravity values except for those for Western Timor and the ITB survey of Tanimbar. Observed values for these surveys were computed by calculating the latitude, free-air and Bouguer corrections and applying these values so,

observed gravity = latitude correction - free-air correction + Bouguer correction + Bouguer anomaly,

to produce a new observed gravity value.

At this point all stations had values for observed gravity, latitude and longitude and height related to the geoid.

The next step was to use the observed gravity values, latitudes, longitudes and heights to compute new anomaly values to match the latest ellipsoidal gravity reduction standard. This standard has been mainly produced by the U.S. Geological Survey and the North American Gravity Database Committee. Useful reference documents are:

Gravity reduction spreadsheet to calculate the Bouguer anomaly using standardized methods and constants. Derek I. Holom and John S. Oldow. Geosphere; April 2007; v. 3; no. 2; p. 86-90; DOI: 10.1130/GES00060.1

New standards for reducing gravity observations: The Revised North American Gravity Database. Hinze et al. 2003.

Rationale and Operational Plan to Upgrade the U.S Gravity Database. Hildenbrand et al.. USGS Open-File Report 02-463, 2002.

The old, gravity reduction standard computed anomalies relative to the geoid (which in practice for Eastern Indonesia meant relative to sea-level): the new standard computes anomalies relative to the ITRF(WGS84) ellipsoid.

It is not necessary to describe in detail all of the steps taken to match the new standard but in summary:

1) all gravity station orthometric elevations (geoid) were recomputed to ITRF(WGS84) ellipsoidal heights using the programs available from the NGA to calculate WGS84/EGM08 geoid undulations

2) the ellipsoid theoretical gravity calculation (also known as the normal, or latitude, correction) used the Somigliana closed-form formula based on the 1980 Geodetic Reference System (GRS80) to calculate the gravity at any latitude

3) the mass of the atmosphere was unaccounted for in the theoretical gravity calculation and was subtracted from the observed gravity value. The atmospheric correction uses the height of the gravity station in metres above the GRS80 ellipsoid

4) free-air Correction - measurements of observed gravity decrease with increasing distance from the center of the Earth. In order to be compared with the theoretical gravity at the same location, the height of the gravity station was corrected to the reference ellipsoid to give the free-air correction.

In summary, points 1-4 result in the reduction of the observed gravity value to a free-air correction anomaly. The next stage was to remove the gravitational effect of the terrain via the Bouguer correction.

 

Complete Bouguer anomaly

The images/maps of the Bouguer anomaly on this web site have been produced using the program FA2Boug.f published by Dr. Javier Fullea. FA2Boug computes the Complete Bouguer anomaly (Bullard A, B and C terrain corrections) using Sandwell and Smith 1 minute topography and gravity grids (http://topex.ucsd.edu/index.htm) and STRM 90 metre land topography grids, both with elevations re-computed and referenced to the ellipsoid, not the geoid. See Data Souces for details.

FA2BOUG – A FORTRAN 90 code to compute bouguer gravity anomalies from gridded free-air anomalies: Application to the atlantic-mediterranean transition zone

J. Fullea, M. Fernàndez and H. Zeyen

Computers and Geosciences

http://dx.doi.org/10.1016/j.cageo.2008.02.018

Javier Fullea's Ph.D. thesis is well worth reading (English) and is available here (3.5mb PDF) .

Use of FA2Boug in this study

FA2Boug operates on 1 minute input grids, not individual gravity stations, and produces Complete Bouguer anomaly grids. The Complete Bouguer anomaly values in the gravity station data files, available for downloading here, have been extracted from the FA2Boug, 1 minute, output grids. This is suitable for this regional study. Also, the Bouguer anomaly surfaces shown in the images and maps on this website were taken from the FA2Boug 1 minute output grids and not re-gridded from the data for individual stations.

The complete Bouguer anomaly grids were computed from free-air anomalies (on the ITRF(WGS84) ellipsoid) for all areas (marine and land. Ellipsoidal terrain correction calculations used the 1 minute topographic grids described above except for Timor, Tanimbar and Kai, where SRTM 90 metre grids were used. For the avoidance of doubt - all topography used in the calculations has been placed relative to the ellipsoid, not the geoid.

The observed gravity values for stations on Timor, Tanimbar and Kai were the original starting points for the reduction process and this means that the historical, local terrain corrections, using Hammer charts have been included again in the complete Bouguer anomaly values. However it is not known if all historical surveys applied Hammer chart terrain corrections (some definitely did not).

FA2Boug uses quarters of a conic prism for terrain calculations in the inner zone which are comparable to Hammer zones. For stations on Tanimbar and Kai the inclusion of the historical Hammer chart corrections is not considered critical, most of the gravity stations being on the coast or on roads or paths running across flat land (usually raised coral platforms). For Timor, a relatively rugged island, the effect might be more important but, as most of the historical terrain correction information has been lost, it is probably preferable to now have a uniform inner zone correction - especially as this correction would be improved if NASA released the 30 metre resolution SRTM data. However, for those stations on Timor in rugged terrain, and for which historical Hammer chart terrain corrections were applied, the Bouger anomaly values will be too high (Hammer chart corrections being additive). Unfortunately it is not possible to calculate, or sensibly estimate, the historical corrections.

The Bouguer correction density for on-shore areas was set at 2.67 gm/cc and 1.027 gm/cc for marine areas.

Preparation for the use of FA2Boug

FA2Boug is expected to operate on free-air gravity grids referenced to the geoid/sea surface but this study has used the latest ellipsoidal gravity reduction standard. Therefore the Sandwell and Smith (S&S) marine gravity grids were manipulated to produce a grid of free-air anomalies referenced to the ITRF (WGS84) ellipsoid.

In this study the S&S marine data gradients and values, within approx. 15km of the coasts of Timor, Tanimbar and Kai, have been altered to produce a gravity surface that honours the on-shore UCL data and forces the near-shore marine data to 'tie-in'. The result is a more smoothly continuous surface at these coastlines, with fewer steps but there are still mis-matches and, occasionally, the 15km start line for the merge operation can be seen in the gravity images.

 

General Map Information